The Petrojet midfielder, who was called up to Egypt's provisional squad for the African Cup of Nations but missed out on the final list, was recently approached by the White Knights.
Shaaban stated that he would like to join Zamalek this winter, but stressed that an exit from the petroleum side has to be by mutual consent.
"Zamalek coach Hossam Hassan called my agent Mohamed Al-Hendi, who told him about my desire to seal a move to the club," Shaban told FilGoal.com.
"I would like to put on the white shirt, but I'm currently under a contract with Petrojet so my club have to accept the offer first."
Zamalek are yet to open talks with Petrojet.
Zamalek board member Hazem Emam and Abdul-Halim Ali, who was appointed as the team's assistant coach last year, initially informed Shaaban of the five-time African champions' interest, the player said.
The 26-year-old was a fringe player last term, but he has established himself as a regular starter at Petrojet in the first half of the current season.
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Petrojet's Shaaban lured by Zamalek approach